{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{\\si}{\\sigma}\n", "\\newcommand{\\al}{\\alpha}\n", "\\newcommand{\\tta}{\\theta}\n", "\\newcommand{\\Tta}{\\Theta}\n", "\\newcommand{\\Si}{\\Sigma}\n", "\\newcommand{\\ld}{\\ldots}\n", "\\newcommand{\\cd}{\\cdots}\n", "\\newcommand{\\Ga}{\\Gamma} \n", "\\newcommand{\\bet}{\\beta}\n", "\\newcommand{\\cU}{\\mathcal{U}}\n", "\\newcommand{\\cN}{\\mathcal{N}}\n", "\\newcommand{\\R}{\\mathbb{R}}\n", "\\newcommand{\\p}{\\mathbb{P}}\n", "\\newcommand{\\f}{\\frac}\n", "\\newcommand{\\ff}{\\frac{1}}\n", "\\newcommand{\\ds}{\\displaystyle}\n", "\\newcommand{\\bE}{\\mathbf{E}}\n", "\\newcommand{\\E}{\\mathbb{E}}\n", "\\newcommand{\\bF}{\\mathbf{F}}\n", "\\newcommand{\\ii}{\\mathrm{i}}\n", "\\newcommand{\\me}{\\mathrm{e}}\n", "\\newcommand{\\hsi}{\\hat{\\sigma}}\n", "\\newcommand{\\hmu}{\\hat{\\mu}}\n", "\\newcommand{\\ste}{\\, ;\\, }\n", "\\newcommand{\\op}{\\operatorname} \n", "\\newcommand{\\argmax}{\\op{argmax}}\n", "\\newcommand{\\lfl}{\\lfloor}\n", "\\newcommand{\\ri}{\\right}\n", "\\newcommand{\\supp}{\\operatorname{supp}}$\n", "\n", "\"Open\n", "\n", "\n", "\n", "# TP Recuit simulé pour le problème du voyageur de commerce\n", "\n", "## Voyageur de commerce\n", "\n", "Dans ce TP, on s'intéresse au problème du [voyageur de commerce](https://fr.wikipedia.org/wiki/Problème_du_voyageur_de_commerce). Etant données $n$ villes, positionnées dans l'espace en positions $V_1, \\ld, V_n$, le problème consiste à trouver une tournée de longueur minimale, c'est-à-dire une permutation $x$ du groupe symétrique $S_n$ minimisant la fonction\n", " $$\n", "x \\in S_n \\longmapsto H(x) := \\sum_{i=1}^n\\op{dist} (V_{x(i)}, V_{x(i+1)})\\;\\;\\text{ où }\\; x(n + 1) := x(1).\n", "$$\n", "La longueur d'une tournée joue le rôle d'énergie ici. \n", "\n", "Ce problème d'optimisation est très simple à décrire mais particulièrement difficile à résoudre.\n", "Une méthode simple consisterait à calculer $H(x)$ pour toutes les permutations $x$. \n", "Mais lorsque $n$ est élevé, cette méthode est irréalisable. C'est le cas dès que le nombre de villes dépasse la dizaine : le cardinal de $S_n$ est de $n!$ (par exemple, pour $n=30$, $n!\\simeq 2.10^{32}$).\n", "\n", "Pour essayer de minimiser H, on propose d'appliquer l'algorithme de recuit simulé en se déplaçant sur $S_n$ aléatoirement de proche en proche, ce qui implique d'avoir, sur $S_n$, une notion d'*éléments voisins* (de *permutations voisines*). Par exemple, on peut considèrer comme voisines deux permutations qui se déduisent l'une de l'autre par la permutation de deux éléments seulement. Cette \"notion de voisinage\" fonctionne, mais dans notre algorithme, nous la remplaçons en fait par une autre, qui permet une convergence plus rapide : nous considérons deux permutations $(x_1,\\ldots, x_n)$, $(y_1,\\ldots, y_n)$ comme voisines si il existe $1\\leq i]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Xvilles,Yvilles = construction_villes(N,\"Ginibre\")\n", "plt.plot(Xvilles,Yvilles,\"b.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. **Calculez une matrice `Distance` contenant toutes les distances 2 à 2 entres les villes (si possible sans boucle for). En position $(i,j)$, la matrice contient la distance entre les villes $i$ et $j$.**" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "Distance = distance_villes(Xvilles,Yvilles)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. **Tirer aléatoirement un trajet initial entre les villes (une permutation $x$ de $\\{1,\\dots,N\\}$) à laide de la commande `np.random.permutation`, et affichez le trajet correspondant.**" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = initialisation_trajet(N)\n", "display_trajet(x,Xvilles,Yvilles)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. **Ecrire une fonction qui à une permutation $x$ associe l'énergie $H(x)$ définie dans le texte. Implémenter l'algorithme du recuit simulé pour trouver une solution au problème du voyageur de commerce.**" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "x,Energies=recuitsimule(x,Distance,Npas,c) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. **Testez l'algorithme pour diverses configurations de villes et affichez le résultat final.** " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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